Wainwright described the cyberattack as an "escalating threat".
"Bearing in mind the impact of the global cyber-attack I would urge people to be patient with staff".
Payment is demanded within three days or the price is doubled, and if none is received within seven days the locked files will be deleted, according to the screen message.
Victims were asked for payment of $300 (275 euros) in the virtual currency Bitcoin.
Anne Rainsberry, NHS incident director, said that the most seriously affected sections were pathology services and imaging services.
He added: "The trust's security measures that we have got in place are stable and still holding firm".
The UK's National Crime Agency's Oliver Gower said: "Cyber criminals may believe they are anonymous but we will use all the tools at our disposal to bring them to justice".
Brad Smith, Microsoft's president and chief legal officer, said in a blog post Sunday that it was in fact the NSA that developed the code being used in the attack.
But he warned it was likely some Australians would fall victim.More news: President Trump Is Interviewing These Four People for FBI Director
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In a blog post, he said: "An equivalent scenario with conventional weapons would be the United States military having some of its Tomahawk missiles stolen".
Microsoft declared the attack a "wake-up call" for governments across the world.
Bossert will also be searching for who is responsible for the first wave of ransomware attacks as well as those involved in a possible second wave.
Symantec said the majority of organizations affected were in Europe.
Over the weekend, the hospital was able to accept patients from other hospitals which were affected - including Broomfield, in Chelmsford, and Colchester - while continuing to maintain a good service thanks to staff across the hospital trust pulling out all the stops to keep it up and running.
On Friday, May 12, 2017, a damaging ransomware attack swept across more than one hundred countries and infected tens of thousands of computers.
Riverbank IT Management managing director Malcolm Newdick said: "Last week's ransomware attack was the most unsafe malware attack we have seen".
Problems with cyber security in the NHS was highlighted a year ago by Dame Fiona Caldicott, the national data guardian, who warned issues were given insufficient priority and that health bodies persisted in using obsolete computer systems, The Times reported.